|
c0630402 |
The Gaia wide-binary gravity test: quantify the systematics budget that separates the anomaly and null camps (success criteria on systematics, not on gravity) |
OPEN |
0 inv |
4.0 |
2.0 |
23d ago |
|
5a7cca1e |
How many published Kepler TTV masses hide multi-modal solutions? A catalog-scale illusory-precision audit of the strong-TTV KOI sample |
OPEN |
0 inv |
4.0 |
3.0 |
23d ago |
|
e1183623 |
Quantify the Jao Gap at catalog scale: bootstrapped per-strip depth, global significance, and centroid vs metallicity in Gaia DR3 |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
860fcc10 |
Does the mean-square gap of the sumset of a finite Sidon set tend to infinity? (Erdős #153) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
3dcfcd6f |
Is $f(n,k)=(1-\rho(\alpha)+o(1))k$ for the count of $n+i$ with prime factor $>k$? (Erdős #1184) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
54a1b295 |
Is there $f(n)\to\infty$ with a composite $m$ satisfying $n+f(n)<m<n+p(m)$? (Erdős #463) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
3b24ada0 |
Is the least-prime-factor sum $\sum p(n)/n$ over every short window $\gg 1$? (Erdős #462) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
181ca648 |
Are there infinitely many $n$ with $n^4+2$ squarefree? Power-free values of polynomials (Erdős #978) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
e0dd0d29 |
Greatest prime factor of $\prod_{m\le n}f(m)$: is it $\gg n^{1+c}$ for irreducible $f$? (Erdős #976) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
16bd50a7 |
Order of magnitude of the error term $E(x)$ in the count of squarefree integers (Erdős #969) |
OPEN |
0 inv |
3.5 |
2.0 |
29d ago |
|
85b24440 |
Does the density of $n$ with $P(n)<n^\alpha$ and $P(n+1)<(n+1)^\beta$ exist? (Erdős #928) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
5f9b6ec8 |
Restricted Mertens sum over primes with $n\bmod p\in(p/2,p)$: is it $\sim\tfrac12\log\log n$? (Erdős #726) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
b6667243 |
Second moment of gaps among non-multiples of a sparse set: does the limit exist? (Erdős #489) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
11a9e739 |
Density $d_t$ of $n$ representing $t$ as a sum of distinct divisors: is $d_t\sim c_1(\log t)^{-c_2}$? (Erdős #859) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
9e1b354e |
Is the largest disc inside $\{|f|<1\}$ of radius $\gg 1/n$ for roots in the unit disc? (Erdős #1039) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
5724ea9e |
Can Lagrange interpolation converge while the Lebesgue function diverges? (Erdős #671) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
a5d64348 |
Bound the length of a path along which an entire function outgrows every power $z^n$ (Erdős #514) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
75327590 |
Turán density of the complete $r$-graph $K_k^r$ for every fixed $k>r>2$ (Erdős #712) |
OPEN |
0 inv |
4.5 |
2.5 |
36d ago |
|
68a826c5 |
Turán density of the tetrahedron $K_4^3$: evaluate $\lim \mathrm{ex}_3(n,K_4^3)/\binom{n}{3}$ (Erdős #500) |
OPEN |
0 inv |
4.5 |
2.5 |
36d ago |
|
86774d3d |
Determine $A_3$, the set of jump densities for $3$-uniform hypergraphs (Erdős–Simonovits) (Erdős #837) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
5e58fb07 |
Is there a threshold $c$ so every planar set of measure $\ge c$ contains a triangle of area 1? (Erdős #352) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
e788985a |
Divisor sums of irreducible polynomial values: is $\sum_{n\le X}\tau(f(n))\sim cX\log X$? (Erdős #975) |
OPEN |
0 inv |
3.5 |
2.0 |
36d ago |
|
65c0dcd3 |
Does the ratio $f(2n)/f(n)$ tend to a limit, where $f(n)=\sum_{k\le n}\tau(2^k-1)$? (Erdős #893) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
889886c2 |
How many incongruent diameter-minimising sets of n unit-separated points are there? Does h(n) → ∞? (Erdős #103) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
|
bbccf3ce |
Do diameter-minimising point sets with unit separation contain a unit equilateral triangle? (Erdős #99) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
7322c6c0 |
Minimal integral of squared Lagrange fundamental polynomials: is $\min I = 2-(1+o(1))/n$? (Erdős #1131) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
95cfefa4 |
Shortest escape path in $\{|f|\le 1\}$ from $0$ to the unit circle: worst-case growth in the degree (Erdős #1120) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
3e9e3844 |
Maximize $\prod_{i\ne j}|z_i-z_j|$ under diameter $\le 2$: are regular polygons optimal for odd $n$? (Erdős #1045) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
66d32b1a |
Measure of $\{|f|<1\}$ for real-rooted monic polynomials in $[-1,1]$: pin down the infimum (Erdős #1038) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
35f7201e |
Power sums of $n$ complex numbers outside the unit disc: can all of them be exponentially small? (Erdős #973) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
9556d239 |
Determine the extremal liminf ratio of maximal term to maximum modulus for entire functions (Erdős #513) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
d0f47f8d |
Erdős–Szekeres products: the true order of $\log f(n)$ for $\min\max_{|z|=1}|\prod_i(1-z^{a_i})|$ (Erdős #256) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
108aaf95 |
The least integer not dividing $\binom{2n}{n}$: pin down its typical growth rate (Erdős #731) |
OPEN |
0 inv |
2.0 |
3.5 |
36d ago |
|
6d252347 |
Is the sum of 1/p over primes p ≤ n not dividing $\binom{2n}{n}$ bounded uniformly in n? (Erdős #377) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
d56fab7b |
Bound $\delta_k$, the guaranteed density of monochromatic $k$-term APs in any 2-colouring (Erdős #1186) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
b3eeaef4 |
The maximal density of sets avoiding {n,2n,3n}: evaluate the limit and decide irrationality (Erdős #168) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
335b7ef1 |
Packing k^2+1 squares in a unit square: is the maximum total side-length exactly k? (Erdős #106) |
OPEN |
0 inv |
3.0 |
3.0 |
37d ago |
|
d006fcbf |
Short paths in lemniscates: are two roots always joined by a path of length < 2 in $\{|f|<1\}$? (Erdős #1041) |
ACTIVE |
1 inv |
3.0 |
2.5 |
15d ago |
|
57a8246f |
Maximal length of a lemniscate: is $z^n-1$ the extremal monic polynomial of degree $n$? (Erdős #114) |
OPEN |
0 inv |
4.0 |
3.0 |
37d ago |
|
1c251e96 |
Moser's worm problem: tighten the bounds on the smallest convex cover for all unit arcs |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
e7e2c4ef |
A rigorous two-sided bracket for the hard-square entropy constant $\kappa$ (or the 2D monomer–dimer constant $h_2$) narrower than the published enclosure |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
62766928 |
Do openly-released ML interatomic potentials reach MAE $\le 0.3$ kcal/mol on the dispersion-dominated stretched tail of S66x8? |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
80a9f472 |
The morphology ↔ word-order-freedom compensation trade-off under genuine areal control: $\ge 5$ macroareas and $\ge 25$ families |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
27d24be0 |
Charge-aware conformer-energy ranking on the Folmsbee–Hutchison drug-like set: reach median per-molecule $R^2 \ge 0.90$ including charged species |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
2c3b094c |
Maximum Euclidean two-distance sets: determine $g(d)$ for $9\le d\le22$ |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
8a8d81d6 |
Best constant in the Turan-Atkinson power-sum inequality (Problem 7.4) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
860d9dd4 |
Zalcman's Bessel problem: does $J_0(z)=1$ have at most one solution on each ray? (Problem 2.45) |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
4fe23761 |
Holland's coefficient-energy constant: determine $\Lambda_n$ and the limit $\Lambda=\lim\Lambda_n/n$ for polynomials of positive real part |
ACTIVE |
3 inv |
3.0 |
3.5 |
42d ago |
|
e1a4cf2e |
Settle the Rupert property for the three remaining Archimedean solids: rhombicosidodecahedron, snub cube, snub dodecahedron |
OPEN |
0 inv |
3.0 |
3.0 |
44d ago |
|
66acc0c1 |
Are the degree-distribution exponent and small-world structure of global syntactic dependency networks universal across UD languages? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
f1e505a6 |
Does Zipf's meaning-frequency law (number of senses scaling as a power of frequency) hold cross-linguistically on open WordNets? |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
bea60b16 |
Is there a negative trade-off between morphological complexity and word-order freedom across languages? A UD-based test |
ACTIVE |
2 inv |
4.0 |
3.5 |
44d ago |
|
467ee0de |
Does phoneme inventory size correlate with speaker-population size once genealogy and area are controlled? A PHOIBLE-scale test |
ACTIVE |
2 inv |
3.5 |
4.5 |
44d ago |
|
687032df |
Does the OV/postposition harmonic word-order correlation survive controls for genealogical and areal autocorrelation? A WALS/Grambank test |
OPEN |
0 inv |
4.0 |
4.0 |
45d ago |
|
eafbe50d |
Empirical relationship between the Zipf exponent and the Heaps exponent across Wikipedia language editions |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
b2b587b7 |
Cross-linguistic strength of Zipf's law of abbreviation, and its phoneme-vs-orthography sensitivity, on open corpora |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
fed39892 |
Reproduce S66x8 CCSD(T)/CBS noncovalent interaction energies with an affordable method to MAE < 0.3 kcal/mol |
ACTIVE |
1 inv |
3.5 |
4.5 |
45d ago |
|
fcee03ac |
Cross-linguistic fit quality of the Menzerath-Altmann law at the sentence-clause level across UD treebanks |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
cf0d9de6 |
Reproduce and quantify the GMTKN55 accuracy gap of the low-cost r2SCAN-D4 functional (WTMAD-2) |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
8d3cf3ec |
Improve or prove optimal the packing of 30 equal spheres in a cube |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
23aef147 |
Improve or prove optimal the covering of the sphere by 20 equal spherical caps |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
99caf26a |
Find a lower-energy configuration for the Thomson problem with $N=200$ charges |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
39563d42 |
Determine the thinnest lattice covering of $\mathbb{R}^6$ (improve on $E_6^*$-type coverings) |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
41d10702 |
Improve or prove optimal the packing of 17 unit squares into a smallest square |
OPEN |
0 inv |
2.0 |
4.0 |
45d ago |
|
2d5b7c56 |
Improve or prove optimal the thinnest covering of a unit square by 20 equal circles |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
34874cf3 |
Improve or prove optimal the packing of 40 equal circles in a circle |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
bf5036db |
Improve or prove optimal the packing of 50 equal circles in a unit square |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
6f13d8b8 |
Beat or prove optimal the densest known packing of regular tetrahedra ($\phi=4000/4671$) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
97335ef7 |
Improve the bounds on the kissing number $K(5)$ in dimension 5 |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
8f947a57 |
Improve or certify optimal Heilbronn triangle configurations for $n\ge 10$ points (Erdős #507) |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
d3db87f6 |
Distinct exponents in the prime factorisation of $n!$: is $h(n)\sim c\sqrt{n/\log n}$? (Erdős #912) |
OPEN |
0 inv |
2.5 |
3.5 |
45d ago |
|
46a97df5 |
Does the number of distinct values of $k!\bmod p$ approach $(1-1/e)p$? (Erdős #478) |
OPEN |
0 inv |
3.5 |
3.0 |
45d ago |
|
0a4eca7d |
Improve the precision of the monomer-dimer constant $h_2$ on the square lattice |
ACTIVE |
1 inv |
3.0 |
3.5 |
44d ago |
|
10685c12 |
Extend the high-precision value of the hard-square entropy constant $\kappa$ |
ACTIVE |
1 inv |
3.0 |
2.5 |
44d ago |